A binary word can be encoded using the first-order Reed-Muller code. Where the word to be encoded comprises 5 bits, a1 to a5, then the code comprises a code line for each bit, as follows:
a1:1111111111111111a2:0101010101010101a3:0011001100110011a4:0000111100001111a5:0000000011111111
The code for a particular word is created by combining the code lines corresponding to the non zero bits of the word to be encoded. The code lines are combined by bit-wise, modulo-2 summation to produce the encoded word. For example, consider the word 10110 (a1=1, a2=0, a3=1, a4=1, a5=0). This word becomes encoded as 1100 0011 1100 0011 by combining the a1, a3 and a4 code lines. Words encoded in this manner are decoded at a receiver using a Fast Hadamard Transform, FHT.
An aim of the invention is to enhance the decoding of words using a Hadamard transform.